There is no unnecessary complication; the question I asked was if there was one genus or two and @Moonhowl
answered the question.
But since Zuzu jumped in to say "If you look at Amaryllis by genus, you will find only two species." I will ask another question if I may...
How is the average person supposed to know which of the many listed on the page are the two species? Are they highlighted in some way? Looking at only the list is there some way to know which are the synonyms? There are 26 plants listed; how do we select the two that are species of Amaryllis and which belong to some other genus.
I know we don't care much for The Plant List but it has 4 plants in the Amaryllis genus with 'accepted' names:
Amaryllis bagnoldii (Herb.) Traub & Uphof
Amaryllis belladonna L.
Amaryllis condenaarit Vargas & Perez
Amaryllis paradisicola Snijman
Looking at The Catalogue of Life I see two plant species in the genus Amaryllis
Amaryllis belladonna L. - accepted name of a plant species
Amaryllis paradisicola Snijman - accepted name of a plant
So that will require me going back and forth to check the many available lists, each claiming to be the correct one. Searching for the truth in taxonomy is like getting stuck between religion and politics.
there is also an Amaryllis genus in the animal world.
Amaryllis - genus in Animalia
Amaryllis macrophthalmus Haswell - accepted name in Animalia (I think it is some kind of sea creature)
Back to our Amaryllis database:
Are Amaryllis belladonna 'Kimberly' and 'Kimberley' the same plant or two different plants?
A. belladonna 'Major', A. b. 'Purpurea', A. b. 'Purpurea major' one, two or three plants?
Is there a listing for Amaryllis belladonna elata? or has that plant been renamed and moved elsewhere?
As I said, now that I know there are two genera, one being Amaryllis and the other being Hippeastrum, there will be more questions about these two lists of plants.
The University of California seems to thing Amaryllis has only once species; other sources say there are two...
more research required. Last night I was too tired and this morning I have work to do so I will leave those questions for another day...or another month.
So you can see what I mean that in answering the question to my satisfaction, @Moonhowl
sparked more questions in my brain. And all this started because I saw a photo of a pretty flower on the internet.
My original question has been answered.